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Full text of "Analytical Mechanics"

MOTION OF A PARTICLE 109 which has a mass of about 453.6 gms. The weight of a body is the force with which it is attracted towards the center of the earth. Therefore if m denotes the mass of a body and g the magnitude of the acceleration which the gravitational attraction of the earth imparts to bodies, the force equation gives us W = mg, (X) where W is the weight of the body. The value of g is slightly different at different points of the surface of the earth. It is greatest at the poles and least at the equator. The maximum variation, however, is less than one per cent; therefore for most purposes it may be considered as constant. For engineering problems 32.2 — '- or 981 ^~ are close sec.2 sec.2 enough approximations to the actual value of g in any locality. The relation between the pound and the dyne may be obtained by the help of equation (X). Thus ft- 1 Ib. = 1 pd. X 32.2 = 32.2 sec.2 sec. = 4.45 X 106 dynes, where "Ib." is the symbol for the pound (weight) and "pd." the symbol for the mass of a body which weighs one pound. In order to emphasize the distinction between the two they are often called pound-weight and pound-mass. 101. Difference between Mass and Weight. — The beginner often finds it difficult to distinguish between the mass of a body and its weight. He is apt to ask such a question as this, "When I buy a pound of fruit what do I get, one